Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1214 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#88098 | C2 | semidirect |
| 2. C22×#88101 | C2 | semidirect |
| 3. C2×#11718279 | C2 | direct (N × H) |
| 7. C22×C13×Q16 | C4 | semidirect |
| 11. C2×#88173 | C4 | semidirect |
| 13. C22×D104 | C4 | semidirect |
| 17. C2×#88101 | C22 | semidirect |
| 19. C2×#88098 | C22 | semidirect |
| 20. #11718279 | C22 | direct (N × H) |
| 34. C2×C13×Q16 | C2×C4 | semidirect |
| 42. #88173 | C2×C4 | semidirect |
| 45. C2×D104 | C2×C4 | semidirect |
| 52. #88101 | C23 | semidirect |
| 54. #88098 | C23 | semidirect |
| 83. C13×Q16 | C22×C4 | semidirect |
| 91. D104 | C22×C4 | semidirect |
| 137. C22×Q16 | #261 | semidirect |
| 148. C22×C13 | #360 | semidirect |
| 178. C2×Q16 | C2×#261 | semidirect |
| 196. C2×C13 | C2×#360 | semidirect |
| 226. Q16 | C22×#261 | semidirect |
| 243. C13 | C22×#360 | semidirect |
| 280. C22 | #11718279 | direct (N × H) |
| 291. C2 | C2×#11718279 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88098 | 2 |
| C22×#88101 | 2 |
| C2×#11718279 | 2 |
| C22×#88173 | 2 |
| C22×#360 | 13 |